Constraint-based graphic statics

This thesis introduces “constraint-based graphic statics”, a geometrical support for computer-aided structural design. This support increases the freedom with which the designer interacts with the plane static equilibriums being shaped. Constraint-based graphic statics takes full advantage of geometry, both its visual expressiveness and its capacity to solve complex problems in simple terms. Accordingly, the approach builds on the two diagrams of classical graphic statics: a form diagram describing the geometry of a strut-and-tie network and a force diagram vectorially representing its inner static equilibrium. Two new devices improve the control of these diagrams: (1) nodes — considered as the only variables — are constrained within Boolean combinations of graphical regions; and (2) the user modifies these diagrams by means of successive operations whose geometric properties do not at any time jeopardise the static equilibrium of the strut-and-tie network. These two devices offer useful features, such as the ability to describe, constrain and modify any static equilibrium using purely geometric grammar, the ability to compute and handle multiple solutions to a problem at the same time, the ability to switch the hierarchy of constraint dependencies, the ability to execute dynamic conditional statements graphically, the ability to compute full interdependency and therefore the ability to remove significantly the limitations of compass-and-straightedge constructions and, finally the ability to propagate some solution domains symbolically. As a result, constraint-based graphic statics encourages the emergence of new structural design approaches that are highly interactive, precognitive and chronology-free: highly interactive because forces and geometries are simultaneously and dynamically steered by the designer; precognitive because the graphical region constraining each points marks out the set of available solutions before they are even explored by the user; and chronology-free because the deductive process undertaken by the designer can be switched whenever desired. Applications cover the design of reticular systems — regardless of whether they are isostatic, indeterminate, prestressed, self-stressed or mechanisms — regular and irregular beams subject to bending, compression-only structures described by lines of thrusts, and structures that can be modelled with discontinuous stress fields.(FSA - Sciences de l'ingénieur) -- UCL, 201